Group #28500046 — subgroups

Subgroups — #28500046

Order 15104.

306 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434680	C₂	1	1	yes	maximal, characteristic
2	#21425898	C₂	1	1	yes	maximal, characteristic
3	#335×D₅₉	C₂	1	1	yes	maximal, characteristic
4	#21422152	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422150	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422145	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1362	C₂	1	1	yes	maximal, characteristic, complemented
8	#16837957	—	2	1	no	—
9	#16837807	C₂²	1	1	yes	characteristic
10	#16837752	—	2	1	no	—
11	#16837640	—	2	1	no	—
12	#16837640	C₄	1	2	yes	—
13	Q₁₆×Dic₅₉	—	2	1	no	—
14	Q₁₆×Dic₅₉	C₄	1	2	yes	—
15	C₄⋊C₈×D₅₉	—	2	1	no	—
16	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
17	C₄⋊(C₅₉⋊C₁₆)	C₂²	1	1	yes	characteristic
18	(C₂×D₅₉)⋊C₁₆	—	2	1	no	—
19	#16837177	—	2	1	no	—
20	#16837155	C₂²	1	1	yes	characteristic
21	#16837154	—	2	1	no	—
22	C₅₉×#494	C₂²	1	1	yes	characteristic
23	C₅₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
24	C₅₉×#335	C₂²	1	1	yes	characteristic
25	C₂×C₈×D₅₉	—	4	1	no	—
26	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
28	#14273727	—	2	1	no	—
29	#14273718	—	4	1	no	—
30	#14273707	—	4	1	no	—
31	#14273703	—	2	2	no	—
32	Q₈×Dic₅₉	—	2	2	no	—
33	#14273692	—	4	1	no	—
34	#14273685	—	4	1	no	—
35	C₄²×D₅₉	D₄	1	1	yes	characteristic
36	C₂×C₅₉⋊C₁₆	—	2	1	no	—
37	#14273661	—	2	1	no	—
38	#14273661	C₂×C₄	1	2	yes	—
39	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
40	Dic₅₉⋊C₈	—	4	1	no	—
41	#14273651	—	2	2	no	—
42	#14273651	—	2	2	no	—
43	C₄×C₅₉⋊C₈	D₄	1	1	yes	characteristic
44	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
45	C₈×Dic₅₉	D₄	1	1	yes	characteristic
46	C₂×Q₁₆×C₅₉	—	2	1	no	—
47	C₂×Q₁₆×C₅₉	C₂×C₄	1	2	yes	—
48	C₄⋊Q₈×C₅₉	—	2	1	no	—
49	C₂×C₁₆×C₅₉	—	2	1	no	—
50	C₄⋊C₈×C₅₉	—	2	1	no	—
51	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
52	C₂×Q₈×C₅₉	—	2	2	no	—
53	C₂×C₄×D₅₉	C₂²⋊C₄	1	1	yes	characteristic
54	C₂×C₄×D₅₉	D₈	1	1	yes	characteristic
55	C₂×C₄×D₅₉	SD₁₆	1	1	yes	characteristic
56	C₂×Dic₁₁₈	—	4	1	no	—
57	Q₁₆×C₅₉	—	4	2	no	—
58	Q₁₆×C₅₉	—	4	1	no	—
59	Q₁₆×C₅₉	—	4	1	no	—
60	C₂×C₈×C₅₉	—	4	1	no	—
61	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
63	C₄⋊C₄×C₅₉	—	4	1	no	—
64	C₄⋊C₄×C₅₉	—	4	1	no	—
65	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
66	(C₂×D₅₉)⋊C₄	—	4	2	no	—
67	C₄⋊Dic₅₉	—	2	2	no	—
68	C₄⋊Dic₅₉	—	4	1	no	—
69	C₄⋊Dic₅₉	—	4	2	no	—
70	Dic₅₉⋊C₄	—	4	2	no	—
71	C₄×Dic₅₉	—	4	2	no	—
72	C₄×Dic₅₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₄×Dic₅₉	D₈	1	1	yes	characteristic
74	C₄×Dic₅₉	SD₁₆	1	1	yes	characteristic
75	C₂×C₅₉⋊C₈	—	4	1	no	—
76	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
78	C₈×D₅₉	—	2	1	no	—
79	C₈×D₅₉	—	2	1	no	—
80	C₈×D₅₉	—	4	1	no	—
81	C₈×D₅₉	—	8	2	no	—
82	C₁₆×C₅₉	—	4	1	no	—
83	C₅₉⋊C₁₆	—	4	1	no	—
84	C₂²×D₅₉	#102	1	1	yes	characteristic
85	Q₈×C₅₉	—	4	2	no	—
86	Q₈×C₅₉	—	4	2	no	—
87	C₂×C₄×C₅₉	—	4	2	no	—
88	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
90	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
91	C₂×Dic₅₉	—	4	2	no	—
92	C₂×Dic₅₉	#102	1	1	yes	characteristic
93	C₂×Dic₅₉	#102	1	1	yes	characteristic
94	C₂×Dic₅₉	#102	1	1	yes	characteristic
95	C₄×D₅₉	—	2	2	no	—
96	C₄×D₅₉	—	2	1	no	—
97	C₄×D₅₉	—	2	1	no	—
98	C₄×D₅₉	—	2	1	no	—
99	C₄×D₅₉	—	2	1	no	—
100	Dic₁₁₈	—	8	1	no	—
101	Dic₁₁₈	—	8	1	no	—
102	C₈×C₅₉	—	2	1	no	—
103	C₈×C₅₉	—	8	1	no	—
104	C₈×C₅₉	#135	1	1	yes	characteristic
105	C₈×C₅₉	#135	1	1	yes	characteristic
106	C₅₉⋊C₈	—	2	1	no	—
107	C₅₉⋊C₈	—	2	1	no	—
108	C₅₉⋊C₈	—	8	1	no	—
109	#11954	—	59	1	no	maximal, Sylow
110	C₂²×C₅₉	C₂×#102	1	1	yes	characteristic
111	C₂×D₅₉	—	2	1	no	—
112	C₂×D₅₉	—	2	1	no	—
113	C₂×D₅₉	#362	1	2	yes	—
114	C₄×C₅₉	—	2	1	no	—
115	C₄×C₅₉	—	8	2	no	—
116	C₄×C₅₉	#413	1	1	yes	characteristic
117	C₄×C₅₉	#416	1	1	yes	characteristic
118	C₄×C₅₉	#509	1	1	yes	characteristic
119	C₄×C₅₉	#510	1	1	yes	characteristic
120	Dic₅₉	—	2	1	no	—
121	Dic₅₉	—	2	1	no	—
122	Dic₅₉	—	2	1	no	—
123	Dic₅₉	—	8	2	no	—
124	#3170	—	59	1	no	—
125	#2163	—	59	1	no	—
126	C₂×#335	—	59	1	no	—
127	#1364	—	59	1	no	—
128	#1364	—	59	1	no	—
129	#1362	—	59	1	no	—
130	#1362	D₅₉	1	1	yes	characteristic, complemented
131	C₂×C₅₉	#1540	1	1	yes	characteristic
132	C₂×C₅₉	#2139	1	1	yes	characteristic
133	C₂×C₅₉	C₂×#362	1	1	yes	characteristic
134	D₅₉	—	2	2	no	—
135	#533	—	118	1	no	—
136	#500	—	59	1	no	—
137	#494	C₂×D₅₉	1	1	yes	characteristic
138	#487	—	118	1	no	—
139	#467	—	59	2	no	—
140	#467	—	118	1	no	—
141	C₄×Q₁₆	—	59	2	no	—
142	C₄×Q₁₆	—	118	1	no	—
143	C₂×C₄⋊C₈	—	118	1	no	—
144	C₂×C₄×C₈	—	59	1	no	—
145	C₄⋊C₁₆	—	59	1	no	—
146	C₄⋊C₁₆	C₂×D₅₉	1	1	yes	characteristic
147	C₂²⋊C₁₆	—	118	1	no	—
148	#346	—	118	1	no	—
149	#335	—	59	1	no	—
150	#335	—	118	1	no	—
151	#335	C₂×D₅₉	1	1	yes	characteristic
152	C₅₉	#11954	1	1	yes	characteristic, complemented, Sylow
153	C₂×Q₁₆	—	2	1	no	—
154	C₂×Q₁₆	C₄×D₅₉	1	2	yes	—
155	C₂²×C₈	—	59	1	no	—
156	C₂²×C₈	—	59	1	no	—
157	C₂²×C₈	—	236	1	no	—
158	C₄⋊Q₈	—	2	1	no	—
159	C₄⋊Q₈	—	118	1	no	—
160	#125	—	236	1	no	—
161	C₂²⋊Q₈	—	118	2	no	—
162	C₂²⋊Q₈	—	236	1	no	—
163	C₄×Q₈	—	118	2	no	—
164	C₄×Q₈	—	236	1	no	—
165	#117	—	236	1	no	—
166	C₂×C₄²	—	59	1	no	—
167	C₂×C₁₆	—	2	1	no	—
168	C₂×C₁₆	—	118	1	no	—
169	#107	—	59	2	no	—
170	#107	—	118	1	no	—
171	C₄⋊C₈	—	2	1	no	—
172	C₄⋊C₈	—	118	1	no	—
173	C₄⋊C₈	—	236	1	no	—
174	#103	—	118	2	no	—
175	#103	—	118	2	no	—
176	C₄×C₈	—	59	1	no	—
177	C₄×C₈	—	59	1	no	—
178	C₄×C₈	—	59	1	no	—
179	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
180	C₂×Q₈	—	2	2	no	—
181	C₂×Q₈	—	236	1	no	—
182	C₂²×C₄	—	59	1	no	—
183	C₂²×C₄	—	59	1	no	—
184	C₂²×C₄	—	59	1	no	—
185	Q₁₆	—	4	2	no	—
186	Q₁₆	—	4	1	no	—
187	Q₁₆	—	4	1	no	—
188	C₂×C₈	—	4	1	no	—
189	C₂×C₈	—	59	1	no	—
190	C₂×C₈	—	59	1	no	—
191	C₂×C₈	—	118	1	no	—
192	C₂×C₈	—	118	1	no	—
193	C₂×C₈	—	472	2	no	—
194	C₂×C₈	—	236	1	no	—
195	C₂×C₈	—	236	1	no	—
196	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
197	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
198	C₄⋊C₄	—	4	1	no	—
199	C₄⋊C₄	—	4	1	no	—
200	C₄⋊C₄	—	118	2	no	—
201	C₄⋊C₄	—	236	2	no	—
202	C₄⋊C₄	—	236	2	no	—
203	C₄⋊C₄	—	236	1	no	—
204	C₂²⋊C₄	—	236	2	no	—
205	C₄²	—	59	1	no	—
206	C₄²	—	59	1	no	—
207	C₄²	—	59	1	no	—
208	C₄²	—	236	2	no	—
209	C₄²	D₄×D₅₉	1	1	yes	characteristic
210	C₁₆	—	4	1	no	—
211	C₁₆	—	236	1	no	—
212	C₂³	—	59	1	no	—
213	Q₈	—	4	2	no	—
214	Q₈	—	4	2	no	—
215	Q₈	—	472	1	no	—
216	Q₈	—	472	1	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	59	1	no	—
219	C₂×C₄	—	59	1	no	—
220	C₂×C₄	—	59	1	no	—
221	C₂×C₄	—	118	2	no	—
222	C₂×C₄	—	118	1	no	—
223	C₂×C₄	—	118	1	no	—
224	C₂×C₄	—	118	1	no	—
225	C₂×C₄	—	118	1	no	—
226	C₂×C₄	—	236	2	no	—
227	C₂×C₄	C₂²⋊C₄×D₅₉	1	1	yes	characteristic
228	C₂×C₄	D₈×D₅₉	1	1	yes	characteristic
229	C₂×C₄	SD₁₆×D₅₉	1	1	yes	characteristic
230	C₈	—	2	1	no	—
231	C₈	—	8	1	no	—
232	C₈	—	118	1	no	—
233	C₈	—	118	1	no	—
234	C₈	—	472	1	no	—
235	C₈	#14273746	1	1	yes	characteristic
236	C₈	#14273748	1	1	yes	characteristic
237	C₂²	—	59	2	no	—
238	C₂²	—	118	1	no	—
239	C₂²	—	118	1	no	—
240	C₂²	#102×D₅₉	1	1	yes	characteristic
241	C₄	—	2	1	no	—
242	C₄	—	8	2	no	—
243	C₄	—	118	1	no	—
244	C₄	—	118	1	no	—
245	C₄	—	118	1	no	—
246	C₄	—	472	2	no	—
247	C₄	#16837383	1	1	yes	characteristic
248	C₄	#16837395	1	1	yes	characteristic
249	C₄	#16837839	1	1	yes	characteristic
250	C₄	#16837844	1	1	yes	characteristic
251	C₂	—	118	2	no	—
252	C₂	#21422742	1	1	yes	characteristic
253	C₂	#21425807	1	1	yes	characteristic
254	C₂	#362×D₅₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21434680

C₂

yes

maximal, characteristic

#21425898

C₂

yes

maximal, characteristic

#335×D₅₉

C₂

yes

maximal, characteristic

#21422152

C₂

yes

maximal, characteristic, complemented

#21422150

C₂

yes

maximal, characteristic, complemented

#21422145

C₂

yes

maximal, characteristic, complemented

C₅₉×#1362

C₂

yes

maximal, characteristic, complemented

#16837957

—

#16837807

C₂²

yes

—

—

C₄

yes

—

Q₁₆×Dic₅₉

—

Q₁₆×Dic₅₉

C₄

yes

—

C₄⋊C₈×D₅₉

—

C₄×C₈×D₅₉

C₂²

yes

characteristic

C₄⋊(C₅₉⋊C₁₆)

C₂²

yes

characteristic

(C₂×D₅₉)⋊C₁₆

—

#16837177

—

#16837155

C₂²

yes

characteristic

#16837154

—

C₅₉×#494

C₂²

yes

characteristic

C₅₉×C₄⋊C₁₆

C₂²

yes

characteristic

C₅₉×#335

C₂²

yes

characteristic

C₂×C₈×D₅₉

—

C₂×C₈×D₅₉

C₂×C₄

yes

characteristic

C₂×C₈×D₅₉

D₄

yes

—

—

—

—

Q₈×Dic₅₉

—

#14273692

—

#14273685

—

C₄²×D₅₉

D₄

yes

characteristic

C₂×C₅₉⋊C₁₆

—

#14273661

—

#14273661

C₂×C₄

yes

—

C₄⋊(C₅₉⋊C₈)

—

Dic₅₉⋊C₈

—

#14273651

—

#14273651

—

C₄×C₅₉⋊C₈

D₄

yes

characteristic

C₈×Dic₅₉

C₂×C₄

yes

characteristic

C₈×Dic₅₉

D₄

yes

characteristic

C₂×Q₁₆×C₅₉

—

C₂×Q₁₆×C₅₉

C₂×C₄

yes

—

C₄⋊Q₈×C₅₉

—

C₂×C₁₆×C₅₉

—

C₄⋊C₈×C₅₉

—

C₄×C₈×C₅₉

C₂³

yes

characteristic

C₂×Q₈×C₅₉

—

C₂×C₄×D₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×D₅₉

D₈

yes

characteristic

C₂×C₄×D₅₉

SD₁₆

yes

characteristic

C₂×Dic₁₁₈

—

Q₁₆×C₅₉

—

Q₁₆×C₅₉

—

Q₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

C₂×D₄

yes

characteristic

(C₂×D₅₉)⋊C₄

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₄×Dic₅₉

C₂²⋊C₄

yes

characteristic

C₄×Dic₅₉

D₈

yes

characteristic

C₄×Dic₅₉

SD₁₆

yes

characteristic

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₈×D₅₉

—

C₈×D₅₉

—

C₈×D₅₉

—

C₈×D₅₉

—

C₁₆×C₅₉

—

C₅₉⋊C₁₆

—

C₂²×D₅₉

#102

yes

characteristic

Q₈×C₅₉

—

Q₈×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₈

yes

characteristic

C₂×C₄×C₅₉

C₂×SD₁₆

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

yes

C₂×Dic₅₉

yes

C₂×Dic₅₉

yes

C₄×D₅₉

—

C₄×D₅₉

—

C₄×D₅₉

—

C₄×D₅₉

—

C₄×D₅₉

—

100

Dic₁₁₈

—

101

Dic₁₁₈

—

102

C₈×C₅₉

—

103

C₈×C₅₉

—

104

C₈×C₅₉

#135

yes

characteristic

105

C₈×C₅₉

#135

yes

characteristic

106

C₅₉⋊C₈

—

107

C₅₉⋊C₈

—

108

C₅₉⋊C₈

—

109

#11954

—

maximal, Sylow

110

C₂²×C₅₉

C₂×#102

yes

characteristic

111

C₂×D₅₉

—

112

C₂×D₅₉

—

113

C₂×D₅₉

#362

yes

—

114

C₄×C₅₉

—

115

C₄×C₅₉

—

116

C₄×C₅₉

#413

yes

characteristic

117

C₄×C₅₉

#416

yes

characteristic

118

C₄×C₅₉

#509

yes

characteristic

119

C₄×C₅₉

#510

yes

characteristic

120

Dic₅₉

—

121

Dic₅₉

—

122

Dic₅₉

—

123

Dic₅₉

—

124

#3170

—

125

#2163

—

126

C₂×#335

—

127

#1364

—

128

#1364

—

129

#1362

—

130

#1362

D₅₉

yes

characteristic, complemented

131

C₂×C₅₉

#1540

yes

characteristic

132

C₂×C₅₉

#2139

yes

characteristic

133

C₂×C₅₉

C₂×#362

yes

characteristic

134

D₅₉

—

135

#533

—

118

—

136

#500

—

137

#494

C₂×D₅₉

yes

characteristic

138

#487

—

118

—

139

#467

—

140

#467

—

118

—

141

C₄×Q₁₆

—

142

C₄×Q₁₆

—

118

—

143

C₂×C₄⋊C₈

—

118

—

144

C₂×C₄×C₈

—

145

C₄⋊C₁₆

—

146

C₄⋊C₁₆

C₂×D₅₉

yes

characteristic

147

C₂²⋊C₁₆

—

118

—

148

#346

—

118

—

149

#335

—

150

#335

—

118

—

151

#335

C₂×D₅₉

yes

characteristic

152

C₅₉

#11954

yes

characteristic, complemented, Sylow

153

C₂×Q₁₆

—

154

C₂×Q₁₆

C₄×D₅₉

yes

—

155

C₂²×C₈

—

156

C₂²×C₈

—

157

C₂²×C₈

—

236

—

158

C₄⋊Q₈

—

159

C₄⋊Q₈

—

118

—

160

#125

—

236

—

161

C₂²⋊Q₈

—

118

—

162

C₂²⋊Q₈

—

236

—

163

C₄×Q₈

—

118

—

164

C₄×Q₈

—

236

—

165

#117

—

236

—

166

C₂×C₄²

—

167

C₂×C₁₆

—

168

C₂×C₁₆

—

118

—

169

#107

—

170

#107

—

118

—

171

C₄⋊C₈

—

172

C₄⋊C₈

—

118

—

173

C₄⋊C₈

—

236

—

174

#103

—

118

—

175

#103

—

118

—

176

C₄×C₈

—

177

C₄×C₈

—

178

C₄×C₈

—

179

C₄×C₈

C₂²×D₅₉

yes

characteristic

180

C₂×Q₈

—

181

C₂×Q₈

—

236

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

Q₁₆

—

186

Q₁₆

—

187

Q₁₆

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

118

—

192

C₂×C₈

—

118

—

193

C₂×C₈

—

472

—

194

C₂×C₈

—

236

—

195

C₂×C₈

—

236

—

196

C₂×C₈

C₂×C₄×D₅₉

yes

characteristic

197

C₂×C₈

D₄×D₅₉

yes

characteristic

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

118

—

201

C₄⋊C₄

—

236

—

202

C₄⋊C₄

—

236

—

203

C₄⋊C₄

—

236

—

204

C₂²⋊C₄

—

236

—

205

C₄²

—

206

C₄²

—

207

C₄²

—

208

C₄²

—

236

—

209

C₄²

D₄×D₅₉

yes

characteristic

210

C₁₆

—

211

C₁₆

—

236

—

212

C₂³

—

213

Q₈

—

214

Q₈

—

215

Q₈

—

472

—

216

Q₈

—

472

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

118

—

222

C₂×C₄

—

118

—

223

C₂×C₄

—

118

—

224

C₂×C₄

—

118

—

225

C₂×C₄

—

118

—

226

C₂×C₄

—

236

—

227

C₂×C₄

C₂²⋊C₄×D₅₉

yes

characteristic

228

C₂×C₄

D₈×D₅₉

yes

characteristic

229

C₂×C₄

SD₁₆×D₅₉

yes

characteristic

230

C₈

—

231

C₈

—

232

C₈

—

118

—

233

C₈

—

118

—

234

C₈

—

472

—

235

C₈

#14273746

yes

characteristic

236

C₈

#14273748

yes

characteristic

237

C₂²

—

238

C₂²

—

118

—

239

C₂²

—

118

—

240

C₂²

#102×D₅₉

yes

characteristic

241

C₄

—

242

C₄

—

243

C₄

—

118

—

244

C₄

—

118

—

245

C₄

—

118

—

246

C₄

—

472

—

247

C₄

#16837383

yes

characteristic

248

C₄

#16837395

yes

characteristic

249

C₄

#16837839

yes

characteristic

250

C₄

#16837844

yes

characteristic

251

C₂

—

118

—

252

C₂

#21422742

yes

characteristic

253

C₂

#21425807

yes

characteristic

254

C₂

#362×D₅₉

yes

characteristic

	subgroup	G/H
center	C₂²	#102×D₅₉
commutator	C₂×C₈×C₅₉	C₂²×C₄
Frattini	C₄×C₈	C₂²×D₅₉
Fitting	C₅₉×#1362	C₂
socle	C₂²×C₅₉	C₂×#102
prime radical	C₂²×D₅₉	#102
cosocle	C₄×C₈×C₅₉	C₂³
hypercenter	#1362	D₅₉
hypocenter	C₅₉	#11954
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #1362

subgroup

G/H

center

C₂²

#102×D₅₉

commutator

C₂×C₈×C₅₉

C₂²×C₄

Frattini

C₄×C₈

C₂²×D₅₉

Fitting

C₅₉×#1362

C₂

C₂²×C₅₉

C₂²×D₅₉

C₄×C₈×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂×C₈×C₅₉ ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #1362

N	H ≅ G/N	type
4. #21422152	C₂	semidirect
5. #21422150	C₂	semidirect
6. #21422145	C₂	semidirect
7. C₅₉×#1362	C₂	semidirect
130. #1362	D₅₉	semidirect
152. C₅₉	#11954	semidirect

H ≅ G/N

type

4. #21422152

C₂

semidirect

5. #21422150

C₂

semidirect

6. #21422145

C₂

semidirect

7. C₅₉×#1362

C₂

semidirect

130. #1362

D₅₉

semidirect

152. C₅₉

#11954

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#21434680	2
#21425898	2
#335×D₅₉	2
#21422152	2
#21422150	2
#21422145	2
C₅₉×#1362	2
#11954	59

subgroup

index

#335×D₅₉

C₅₉×#1362

Subgroups — #28500046

Conjugacy classes of subgroups

Complements

Maximal subgroups